Warp zones do count--but with some major caveats.
Each non-character warp zone lowers your total time by 15 seconds, and speed-running the Commander Video and Flywrench warp zones can lower your time by ~7 seconds combined--for a grand total of about 230 seconds.
On XBLA, the bonus time won't get subtracted from your total until you've improved a time on a normal level (after running the warp zones). On Steam, the time gets subtracted immediately.
However, the bonuses don't last. Once you restart the game, the bonuses disappear after you improve another level--meaning that to keep your time low, you have to redo all the warp zones every time you play.
Personally, I wouldn't bother with them unless you're not planning to play the game for a while and want your time to be as low as possible while you're away. (This is what I'm doing on XBLA while I play the Steam version).
It didn't always work this way on XBLA. Before the update came out three weeks ago, the bonus time didn't disappear when you restarted the game. If your previous time was ~3000 seconds (and you haven't played since the update), you can probably expect it to jump up by about 230 seconds (possibly more if you have any 0 times--the update corrects those), and rerunning the warp zones will just get you down to where you used to be.
On the other hand, the update also allows you to reach 310 levels completed, so you can expect your leaderboard position to improve, regardless of whether it adds on time.
Hope this helps.